{"id":"https://openalex.org/W7130589178","doi":"https://doi.org/10.48550/arxiv.2602.15965","title":"FLoPS: Semantics, Operations, and Properties of P3109 Floating-Point Representations in Lean","display_name":"FLoPS: Semantics, Operations, and Properties of P3109 Floating-Point Representations in Lean","publication_year":2026,"publication_date":"2026-02-17","ids":{"openalex":"https://openalex.org/W7130589178","doi":"https://doi.org/10.48550/arxiv.2602.15965"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.15965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.15965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126369506","display_name":"Tung-Che Chang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Tung-Che","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124039540","display_name":"Sehyeok Park","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, Sehyeok","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126417824","display_name":"Jay P Lim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lim, Jay P","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011881274","display_name":"Santosh Nagarakatte","orcid":"https://orcid.org/0000-0002-5048-8548"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nagarakatte, Santosh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.6230999827384949},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.49619999527931213},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4959000051021576},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.4641000032424927},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.4255000054836273},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.38109999895095825},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.3637999892234802}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6448000073432922},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6230999827384949},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5329999923706055},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.49619999527931213},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38019999861717224},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3474000096321106},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C116253237","wikidata":"https://www.wikidata.org/wiki/Q1437424","display_name":"Formal specification","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.15965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.15965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"upcoming":[1],"IEEE-P3109":[2],"standard":[3],"for":[4,159,172],"low-precision":[5],"floating-point":[6],"arithmetic":[7],"can":[8],"become":[9],"the":[10,85,111,115,127,155],"foundation":[11,171],"of":[12,41,51,84,94,110,139,154,164,180],"future":[13,181],"machine":[14],"learning":[15],"hardware":[16],"and":[17,31,61,122,176,190],"software.":[18,183],"Unlike":[19],"IEEE-754,":[20],"P3109":[21,86,95,128,175],"introduces":[22],"a":[23,37,67,90,102,136,169],"parametric":[24],"framework":[25],"defined":[26],"by":[27,118],"bitwidth,":[28],"precision,":[29],"signedness,":[30],"domain.":[32],"This":[33,77,166],"flexibility":[34],"results":[35],"in":[36,82,96],"vast":[38],"combinatorial":[39],"space":[40],"formats":[42,160],"--":[43,53],"some":[44],"with":[45,161],"as":[46,48,58,101],"little":[47],"one":[49,162],"bit":[50,163],"precision":[52],"alongside":[54],"novel":[55,137],"features":[56],"such":[57],"stochastic":[59],"rounding":[60,148],"saturation":[62,145],"arithmetic.":[63],"These":[64],"deviations":[65],"create":[66],"unique":[68],"verification":[69,179],"gap":[70],"that":[71,106,133],"this":[72],"paper":[73,78],"intends":[74],"to":[75],"address.":[76],"presents":[79],"FLoPS,":[80],"Formalization":[81],"Lean":[83,185],"Standard,":[87],"which":[88],"is":[89,187],"comprehensive":[91],"formal":[92,178],"model":[93],"Lean.":[97],"Our":[98,184],"work":[99,167],"serves":[100],"rigorous,":[103],"machine-checked":[104],"specification":[105],"facilitates":[107],"deep":[108],"analysis":[109],"standard.":[112],"We":[113],"demonstrate":[114],"model's":[116],"utility":[117],"verifying":[119],"foundational":[120],"properties":[121,153],"analyzing":[123],"key":[124],"algorithms":[125],"within":[126],"context.":[129],"Specifically,":[130],"we":[131],"reveal":[132],"FastTwoSum":[134],"exhibits":[135],"property":[138],"computing":[140],"exact":[141],"\"overflow":[142],"error\"":[143],"under":[144],"using":[146],"any":[147],"mode,":[149],"whereas":[150],"previously":[151],"established":[152],"ExtractScalar":[156],"algorithm":[157],"fail":[158],"precision.":[165],"provides":[168],"verified":[170],"reasoning":[173],"about":[174],"enables":[177],"numerical":[182],"development":[186],"open":[188],"source":[189],"publicly":[191],"available.":[192]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-02-20T00:00:00"}